tmp/tmpeeklk4a6/{from.md → to.md}
RENAMED
|
@@ -0,0 +1,16 @@
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 1 |
+
#### Incomplete elliptic integral of the first kind <a id="sf.cmath.ellint.1">[[sf.cmath.ellint.1]]</a>
|
| 2 |
+
|
| 3 |
+
``` cpp
|
| 4 |
+
double ellint_1(double k, double phi);
|
| 5 |
+
float ellint_1f(float k, float phi);
|
| 6 |
+
long double ellint_1l(long double k, long double phi);
|
| 7 |
+
```
|
| 8 |
+
|
| 9 |
+
*Effects:* These functions compute the incomplete elliptic integral of
|
| 10 |
+
the first kind of their respective arguments `k` and `phi` (`phi`
|
| 11 |
+
measured in radians).
|
| 12 |
+
|
| 13 |
+
*Returns:* $$\mathsf{F}(k, \phi) =
|
| 14 |
+
\int_0^\phi \! \frac{\mathsf{d}\theta}{\sqrt{1 - k^2 \sin^2 \theta}}
|
| 15 |
+
\text{ ,\quad for $|k| \le 1$,}$$ where k is `k` and φ is `phi`.
|
| 16 |
+
|